Question: Emma and Alex are organizing two different weekly clubs. Emma’s club meets every 6 days, while Alex’s club meets every 8 days. They both attended their clubs today. In how many days will both clubs meet on the same day again?
A) 24 days
B) 48 days
C) 12 days
D) 30 days
Solution:
To find when both clubs will meet on the same day again, we need to find the LCM of 6 and 8.
Prime Factorization:
6 = 2 × 3
8 = 2³
LCM Calculation:
Take the highest power of each prime factor :
For 2:2³
For 3:3¹
LCM = 2³ × 3¹ = 8 × 3 = 24
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